A new approximation for ocean waves propagating over a beach with variable depth

In this paper, the phenomenon of ocean waves propagating over a beach with variable water depth is re-examined. Based on the assumption of shallow water, a linearised shallow water equation is solved with an arbitrary beach profile. These irregular beach profiles form a set of partial differential equation with variable coefficient as the governing equation, which is the main obstacle in obtaining analytical solutions. In this paper, two families of beach profile are used as examples. A parametric study is conducted to investigate the influence of the beach profiles on the water surface elevation (η) and velocities (u).